This is a Phase I protocol for patients with cancer involving the liver and porta hepatis using escalating dose rates of BUdR, a thymidine analog radiosensitizer, combined with hyperfractionated external beam irradiation. Radiation dose is determined through the use of three dimensional treatment planning techniques and is based on the volume of normal liver spared, in a manner identical to a previous version of 719 (however, the radiation doses have been decreased in this current protocol).